New variable separation solutions and nonlinear phenomena for the (2+1)-dimensional modified Korteweg–de Vries equation |
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Institution: | 1. School of Computer Science, Shaanxi Normal University, Xi’an 710119, China;2. School of Physical Science and Technology, Ningbo University, Ningbo 315211, China;1. School of Computer Science, Shaanxi Normal University, Xi’an, Shaanxi 710119, China;2. School of Physical Science and Technology, Ningbo University, Ningbo, Zhejiang 315211, China |
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Abstract: | Variable separation approach, which is a powerful approach in the linear science, has been successfully generalized to the nonlinear science as nonlinear variable separation methods. The (2 + 1)-dimensional modified Korteweg–de Vries (mKdV) equation is hereby investigated, and new variable separation solutions are obtained by the truncated Painlevé expansion method and the extended tanh-function method. By choosing appropriate functions for the solution involving three low-dimensional arbitrary functions, which is derived by the truncated Painlevé expansion method, two kinds of nonlinear phenomena, namely, dromion reconstruction and soliton fission phenomena, are discussed. |
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